Adding, subtracting and finding the least common multiple
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This solution deals with adding, subtracting and finding the least common multiple.
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- Adding, subtracting and finding the least common multiple
Step by Step Solution
Step 1 :
4
Simplify —
7
Equation at the end of step 1 :
3 5 4
(—— - ——) + —
27 12 7
Step 2 :
5
Simplify ——
12
Equation at the end of step 2 :
3 5 4
(—— - ——) + —
27 12 7
Step 3 :
1
Simplify —
9
Equation at the end of step 3 :
1 5 4
(— - ——) + —
9 12 7
Step 4 :
Calculating the Least Common Multiple :
4.1 Find the Least Common Multiple
The left denominator is : 9
The right denominator is : 12
| Prime Factor | Left Denominator | Right Denominator | L.C.M = Max {Left,Right} |
|---|---|---|---|
| 3 | 2 | 1 | 2 |
| 2 | 0 | 2 | 2 |
| Product of all Prime Factors | 9 | 12 | 36 |
Least Common Multiple:
36
Calculating Multipliers :
4.2 Calculate multipliers for the two fractions
Denote the Least Common Multiple by L.C.M
Denote the Left Multiplier by Left_M
Denote the Right Multiplier by Right_M
Denote the Left Deniminator by L_Deno
Denote the Right Multiplier by R_Deno
Left_M = L.C.M / L_Deno = 4
Right_M = L.C.M / R_Deno = 3
Making Equivalent Fractions :
4.3 Rewrite the two fractions into equivalent fractions
Two fractions are called equivalent if they have the same numeric value.
For example : 1/2 and 2/4 are equivalent, y/(y+1)2 and (y2+y)/(y+1)3 are equivalent as well.
To calculate equivalent fraction , multiply the Numerator of each fraction, by its respective Multiplier.
L. Mult. • L. Num. 4 —————————————————— = —— L.C.M 36 R. Mult. • R. Num. 5 • 3 —————————————————— = ————— L.C.M 36
Adding fractions that have a common denominator :
4.4 Adding up the two equivalent fractions
Add the two equivalent fractions which now have a common denominator
Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:
4 - (5 • 3) -11
——————————— = ———
36 36
Equation at the end of step 4 :
-11 4
——— + —
36 7
Step 5 :
Calculating the Least Common Multiple :
5.1 Find the Least Common Multiple
The left denominator is : 36
The right denominator is : 7
| Prime Factor | Left Denominator | Right Denominator | L.C.M = Max {Left,Right} |
|---|---|---|---|
| 2 | 2 | 0 | 2 |
| 3 | 2 | 0 | 2 |
| 7 | 0 | 1 | 1 |
| Product of all Prime Factors | 36 | 7 | 252 |
Least Common Multiple:
252
Calculating Multipliers :
5.2 Calculate multipliers for the two fractions
Denote the Least Common Multiple by L.C.M
Denote the Left Multiplier by Left_M
Denote the Right Multiplier by Right_M
Denote the Left Deniminator by L_Deno
Denote the Right Multiplier by R_Deno
Left_M = L.C.M / L_Deno = 7
Right_M = L.C.M / R_Deno = 36
Making Equivalent Fractions :
5.3 Rewrite the two fractions into equivalent fractions
L. Mult. • L. Num. -11 • 7 —————————————————— = ——————— L.C.M 252 R. Mult. • R. Num. 4 • 36 —————————————————— = —————— L.C.M 252
Adding fractions that have a common denominator :
5.4 Adding up the two equivalent fractions
-11 • 7 + 4 • 36 67
———————————————— = ———
252 252
Final result :
67
——— = 0.26587
252
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